# Jürgen Herzog: Rings of Teter type

Time: Mon 2022-05-09 16.30 - 17.30

Location: Zoom

Video link: Meeting ID: 644 6390 5038

Lecturer: Jürgen Herzog (Duisburg-Essen)

### Abstract

A 0-dimensional local ring $$(R,m_R)$$ is called a Teter ring, if there exists a local Gorenstein ring $$(G,m_G)$$ such that R is isomorphic to $$G/(0:m_G)$$. This class of rings has been introduced 1974 by William Teter. It has been shown by Huneke and others that a local ring R is a Teter ring if and only if there exists an epimorphism $$\varphi:\omega_R\to m_R$$. Here $$\omega_R$$ denotes the canonical module of R. The ring is called of Teter type, if there exists a surjective homomorphism from $$\omega_R$$ onto the trace of $$\omega_R$$. Various classes of algebras of Teter type will be considered.

This is joint work with Oleksandra Gasanova, Takayuki Hibi and Somayeh Moradi.